A(3,5) and b(9,-3) lie on a circle. show that the centre of the circle lies on the line 4y-3x+14 = 0
Is it possible to work out the centre of the circle algebraically since the only method I can think of is drawing the points and the line on a set of axis and estimating the circle's radius.
that was my attempt; ie I worked out the centre by plotting the points and then estimating it. helpfully the centre in this question was a whole number but I want to know how to answer the question properly(give an algebraic solution)
Best Answer
A middle point of $AB$ it's $(6,1)$ and $$m_{AB}=\frac{5+3}{3-9}=-\frac{4}{3}.$$ Thus, a center of the circle is placed on $$y-1=\frac{3}{4}(x-6)$$ or $$4y-3x+14=0.$$